Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 1 (2006), 309-327.
A rational splitting of a based mapping space
Let be the space of base-point-preserving maps from a connected finite CW complex to a connected space . Consider a CW complex of the form and a space whose connectivity exceeds the dimension of the adjunction space. Using a Quillen–Sullivan mixed type model for a based mapping space, we prove that, if the bracket length of the attaching map is greater than the Whitehead length of , then has the rational homotopy type of the product space . This result yields that if the bracket lengths of all the attaching maps constructing a finite CW complex are greater than and the connectivity of is greater than or equal to , then the mapping space can be decomposed rationally as the product of iterated loop spaces.
Algebr. Geom. Topol., Volume 6, Number 1 (2006), 309-327.
Received: 19 July 2005
Revised: 14 February 2006
Accepted: 14 February 2006
First available in Project Euclid: 20 December 2017
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Kuribayashi, Katsuhiko; Yamaguchi, Toshihiro. A rational splitting of a based mapping space. Algebr. Geom. Topol. 6 (2006), no. 1, 309--327. doi:10.2140/agt.2006.6.309. https://projecteuclid.org/euclid.agt/1513796514